A. Individual Spot Colors (Solids and Tints)
Workflows and proofing systems such as Prinergy™/Evo, Veris™, and InSite™, known in the art, typically provide a means to support spot colors, i.e., extra printing inks beyond the normal cyan, magenta, yellow, and black (“CMYK”) process colors. (Prinergy and Veris are Trademarks of Eastman Kodak Company, Rochester, N.Y.). A standard list of color names and their solid L*a*b* measurements, such as the Pantone™ library, have been provided as a way to identify spot colors. (Pantone is a Trademark of Pantone, Inc., a Corporation of Delaware located at 590 Commerce Boulevard, Carlstadt, N.J. 07072-3098.) Colors not included in these standard lists can be identified by users capable of providing CIELAB or spectral measurements of such colors. Conventional historical proofing systems, such as the Rainbow™ Desktop Proofing System, provided users with the ability to add CIELAB measurements of not only solid spot colors, but tinted (i.e. less than 100% density) spot colors also. (Rainbow is a Trademark of Kodak Polychrome Graphics, an LLC of Delaware located at 401 Merritt #7 Norwald, Conn. 06851.) These conventional proofing systems could perform simple spline interpolations in order to simulate the printed appearance of such tinted spot colors.
Spot color processing is typically performed by raster image processing (“RIPing”) an EPS or PDF file, known in the art, containing red-green-blue (“RGB”) or CMYK images as well as vector objects containing spot colors. If the destination is a press with only CMYK inks, the vector objects are converted to CMYK approximations, which are often embedded in the file with the spot color names. If the destination press actually supports the requested spot color inks, the file is RIPed into a separate bit map plane for C, M, Y, and K, as well as a separate bit map plane for each destination spot color.
However, these conventional workflows and proofing systems have limitations when spot colors are used. One shortcoming is that although good color management infrastructure exists for handling CMYK, the same is not true for spot colors. For example, if a file prepared for standard SWOP requires conversion for printing on newsprint, CMYK images can be converted using a specific source and destination profile. However, it is difficult to convert spot colors properly since such a conversion requires the equivalent of a unique profile for each spot color for both source and destination.
Another shortcoming is that in the conventional workflows and proofing systems, accurately proofing or estimating the appearance of spot colors after printing is challenging both in terms of infrastructure and measurements required. In particular, the number of calculations involved in the estimating and the size of the look-up-tables (LUTs) needed for the calculations increase exponentially with every additional color added to the mix. For example, if four colors, C, M, Y, K, are printed, the number of calculations and the size of the LUTs are derived from a number raised to an exponent of four, whereas if five colors, C, M, Y, K, plus one spot color are printed, the number of calculations and the size of the LUTs are derived from a number raised to an exponent of five. This shortcoming is compounded when using a single database of spot color values for use in many different print conditions that differ in dot gain, substrate color, etc.
Yet another shortcoming is that even expensive contract proofing systems cannot print sharp, well-defined dots as compared with actual print jobs on a press that often result in very soft-edged dots, which may in fact demonstrate a slight smearing of the dots, which reduces their ink film thickness and which may also stain the non-imaged region adjacent to the dot. (Accordingly, “smearing” and “staining” effects often are referred to interchangeably herein.) By viewing such print jobs under a magnifying glass, one can often detect that the density of dots is somewhat less than that of solid. As illustrated with FIGS. 5 and 6, one can also detect that the “holes” of the halftone screen (i.e. areas where substrate is visible in between the colorant dots) are stained by the ink used to print the dots. Hence, the maximum density Dmax of the dots is reduced whereas the minimum density Dmin of the adjacent substrate holes is increased by ink stain, both due to the phenomenon of dot or ink smearing. Visually, this phenomenon results in spot color tints that are potentially “cleaner” (i.e., higher L* for a given C*) as well as potentially shifted in hue on the print job from the press as compared to the halftone proof.
Accordingly, a need in the art exists for improved color management and proofing techniques pertaining to the use of spot colors.
B. Mixing of Colors
For many years, algorithms and applications have existed for estimating the result of printing and mixing halftone dots, as well as for mixing paints, dyes, etc. Generally, these calculations have been spectrally-based, meaning that full spectral information (as opposed to tristimulous data) was required regarding both colorants and substrates in order to estimate how they would add together to create a resulting color.
These methods have been used to create characterizations of N color printing systems where the ink sets are fixed. For CMYK, or N=4 systems, very accurate characterizations and corresponding ICC profiles have been generated by many products such as Kodak Profile Wizard and Gretag ProfileMaker using standard four-color charts such as IT8.7/4:2005 which has 1617 patches. For larger values of N, such as seven-color ink systems, products are now available to create seven-color ICC profiles using custom charts. The challenge with such characterizations is that the sampling of the seven color space is extremely sparse with higher dimensionality and that the sampling of the multidimensional grid of the ICC profile is also very sparse (typically a grid sampling of three or four per dimension rather than 17). This sparse sampling of both characterization data and of the corresponding profile can lead to inaccuracies in both proofing and color conversions.
For N-color printing systems where the color set is not fixed, the existing problem facing users of spot colors is far more complicated. There may be hundreds or thousands of spot colors in the spot color database. In order to achieve comparable quality to an ICC profile built from CMYK charts, an astronomical number of color combinations and measurements would have to be performed.
One conventional scheme for modeling N-color printing systems was introduced by Vigianno in 1990 with the work, “Modeling the Color of Multi-Color Halftones”, TAGA Proceedings, p. 44-62, Technical Association of the Graphic Arts, 1990. This work defined new spectral Neugebauer equations, which combined spectral Neugebauer:
                                          R            ⁡                          (              λ              )                                =                                    ∑                              j                ,                k                ,                l                ,                                  m                  =                  0                                                            j                ,                k                ,                l                ,                                  m                  =                  1                                                      ⁢                                                  ⁢                                                            R                  ⁡                                      (                    λ                    )                                                  jklm                            ⁢                              a                jklm                                                    ⁢                                  ⁢        for        ⁢                                  ⁢                              j            =            0                    ,                      1            =                                          >                C                            =              0                                ,          1.0                ⁢                                  ⁢                              k            =            0                    ,                      1            =                                          >                M                            =              0                                ,          1.0                ⁢                                  ⁢                              l            =            0                    ,                      1            =                                          >                M                            =              0                                ,          1.0                ⁢                                  ⁢                              m            =            0                    ,                      1            =                                          >                K                            =              0                                ,          1.0                                    Eq        .                                  ⁢        1            
with a dot gain correction:ap=af+2Δp[af(1−af)]1/2  Eq. 2
with the Yule-Nielson correction:R=[(1−k)Rpμ+kRkμ]n  Eq. 3
The modified expression for R is substituted in the summation over all the R's in equation 1. These equations provide a way to estimate the resulting appearance of mixed or overprinted halftone dots of different colors.
Estimating the resulting appearance of mixed solid inks of varying thicknesses was addressed by Kubelka-Munk in, “Modeling Ink-Jet Printing: Does Kubelka-Munk Theory Apply?”, L. Yang Proc. IS&T NIP18 Conf. 482-485, Sep. 29-Oct. 4, 2002, San Diego, Calif., USA. The Kubelka-Munk equation defines reflectance for multiple colorants on a substrate, where the colorants have both an absorption coefficient (k) and a scattering coefficient (s) as a function of wavelength λ.
                                          R            ⁡                          (                              λ                ,                z                            )                                =                                                                      (                                                            R                      ∞                                        -                                          R                      g                                                        )                                ⁢                                  ⅇ                                                            -                                              (                                                                              1                            /                                                          R                              ∞                                                                                -                                                      R                            ∞                                                                          )                                                              ⁢                    sz                                                              -                                                R                  ∞                                ⁡                                  (                                      1                    -                                                                  R                        g                                            ⁢                                              R                        ∞                                                                              )                                                                                                                          R                    ∞                                    ⁡                                      (                                                                  R                        ∞                                            -                                              R                        g                                                              )                                                  ⁢                                  ⅇ                                                            -                                              (                                                                              1                            /                                                          R                              ∞                                                                                -                                                      R                            ∞                                                                          )                                                              ⁢                    sz                                                              -                              (                                  1                  -                                                            R                      g                                        ⁢                                          R                      ∞                                                                      )                                                    ⁢                                  ⁢        where                            Eq        .                                  ⁢        4                                          R          ∞                =                  1          +                                    k              ⁡                              (                λ                )                                                    s              ⁡                              (                λ                )                                              -                                                                      (                                                            k                      ⁡                                              (                        λ                        )                                                                                    s                      ⁡                                              (                        λ                        )                                                                              )                                2                            +                              2                ⁢                                                      k                    ⁡                                          (                      λ                      )                                                                            s                    ⁡                                          (                      λ                      )                                                                                                                              Eq        .                                  ⁢        5            
The conventional calculations, discussed above, are useful when full spectral data is known for each of the colors being mixed and if one has information characterizing k(λ) and s(λ). However, one often does not have full spectral data particularly in an ICC workflow (which is inherently L*a*b* centric). Often one only has a generic set of measured color data printed on one substrate stock for the colors being mixed, such as measured CIELAB data. Accordingly, a need in the art exists for an accurate way to estimate the resulting appearance or color of individual spot colors on various substrate stocks without having to physically measure the appearance of each of the colors to be mixed on such various substrate stocks. The need likewise exists to estimate a reasonable estimate of the solid overprints of spot colors even when only the generic data above is available.
Furthermore, even if one has spectral data for each individual colorant, typically one does not have a definition for k(λ) and s(λ). Conventional methods typically involve printing each colorant against (at least) a black background as well as white, measuring the spectra of each in order to infer these functions of λ. Indeed, if such data is available, inferring the above expressions is relatively easy. However, obtaining such measurements may not be practical.
A reason why existing methods of profiling spot colors have been limited in quality or unreasonably complex to implement, is because there has been lacking a good fundamental model that describes the printing processes being used. If a truly valid model can be constructed, typically one can estimate the behavior of a process using a very small number of parameters that each have an associated physical correlation to the system being characterized. In the event that certain properties must be characterized with a function of wavelength (for example the combined effects of for k(λ) and s(λ), or other wavelength effects such as internal reflection between colorant layers which is dependent on the index of refraction n(λ)) one can still ascertain this information via least squares fit to actual data using the accurate physical model.
Such a model would be of value because static N-color profiles (profiles of fixed colorant sets) can be more effectively created using less measurement with maximum accuracy. Even if overprints are only estimated imperfectly by the proposed model, it can be easily corrected empirically using inter-channel correction factors in order to achieve a high degree of accuracy. This is due to the fact that the Neugebauer primaries (i.e. the various possible combinations of solid colorants) are well-defined and are available for measurement in the form of test charts.
Accordingly, a need in the art exists for a good fundamental model and implementations thereof that describes the printing processes being used.